The Influence of Semantic Magnitude Representations on Arithmetic: Theory, Data, and Simulation

Arithmetic research reveals longer RTs for large problems (6x8) than small problems (2x3). While several factors have been implicated, they cannot be dissociated in normal arithmetic. Subjects were trained on an artificial operation designed to independently manipulate these variables. Results suggest that semantic operand representations and presentation frequency are involved. A new theory of arithmetic fact retrieval is introduced which suggests that arithmetic facts are stored and retrieved using a magnitude representation of the problem operands. Simulations suggest the theory is able to account for the major arithmetic fact retrieval phenomena.